TSTP Solution File: SET599+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:20:37 EDT 2022
% Result : Theorem 2.18s 1.18s
% Output : Proof 2.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 21:29:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.36/0.90 Prover 0: Preprocessing ...
% 1.69/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.83/1.08 Prover 0: Constructing countermodel ...
% 2.18/1.18 Prover 0: proved (554ms)
% 2.18/1.18
% 2.18/1.18 No countermodel exists, formula is valid
% 2.18/1.18 % SZS status Theorem for theBenchmark
% 2.18/1.18
% 2.18/1.18 Generating proof ... Warning: ignoring some quantifiers
% 2.47/1.32 found it (size 9)
% 2.47/1.32
% 2.47/1.32 % SZS output start Proof for theBenchmark
% 2.47/1.32 Assumed formulas after preprocessing and simplification:
% 2.47/1.32 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (difference(v0, v1) = v2 & symmetric_difference(v0, v1) = v3 & ~ subset(v2, v3) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v5, v4) = v7) | ~ (difference(v4, v5) = v6) | ~ (union(v6, v7) = v8) | symmetric_difference(v4, v5) = v8) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (difference(v7, v6) = v5) | ~ (difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (symmetric_difference(v7, v6) = v5) | ~ (symmetric_difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v7) | ~ member(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v4) | member(v6, v7) | member(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v5, v4) = v6) | union(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | union(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | subset(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (symmetric_difference(v5, v4) = v6) | symmetric_difference(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (symmetric_difference(v4, v5) = v6) | symmetric_difference(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (symmetric_difference(v4, v5) = v6) | ? [v7] : ? [v8] : (difference(v5, v4) = v8 & difference(v4, v5) = v7 & union(v7, v8) = v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ member(v6, v4) | ~ subset(v4, v5) | member(v6, v5)) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : (( ~ member(v6, v5) | ~ member(v6, v4)) & (member(v6, v5) | member(v6, v4)))) & ? [v4] : ? [v5] : (subset(v4, v5) | ? [v6] : (member(v6, v4) & ~ member(v6, v5))) & ? [v4] : subset(v4, v4))
% 2.76/1.36 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.76/1.36 | (1) difference(all_0_3_3, all_0_2_2) = all_0_1_1 & symmetric_difference(all_0_3_3, all_0_2_2) = all_0_0_0 & ~ subset(all_0_1_1, all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : subset(v0, v0)
% 2.76/1.36 |
% 2.76/1.36 | Applying alpha-rule on (1) yields:
% 2.76/1.36 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2))
% 2.76/1.36 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 2.76/1.37 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 2.76/1.37 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 2.76/1.37 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 2.76/1.37 | (7) ? [v0] : subset(v0, v0)
% 2.76/1.37 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 2.76/1.37 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 2.76/1.37 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0))
% 2.76/1.37 | (11) symmetric_difference(all_0_3_3, all_0_2_2) = all_0_0_0
% 2.76/1.37 | (12) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 2.76/1.37 | (13) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 2.76/1.37 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 2.76/1.37 | (15) ~ subset(all_0_1_1, all_0_0_0)
% 2.76/1.37 | (16) difference(all_0_3_3, all_0_2_2) = all_0_1_1
% 2.76/1.37 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 2.76/1.37 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2))
% 2.76/1.37 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1))
% 2.76/1.37 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0))
% 2.76/1.37 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 2.76/1.37 |
% 2.76/1.37 | Instantiating formula (18) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms symmetric_difference(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 2.76/1.37 | (22) ? [v0] : ? [v1] : (difference(all_0_2_2, all_0_3_3) = v1 & difference(all_0_3_3, all_0_2_2) = v0 & union(v0, v1) = all_0_0_0)
% 2.76/1.37 |
% 2.76/1.37 | Instantiating (22) with all_13_0_9, all_13_1_10 yields:
% 2.76/1.37 | (23) difference(all_0_2_2, all_0_3_3) = all_13_0_9 & difference(all_0_3_3, all_0_2_2) = all_13_1_10 & union(all_13_1_10, all_13_0_9) = all_0_0_0
% 2.76/1.37 |
% 2.76/1.37 | Applying alpha-rule on (23) yields:
% 2.76/1.37 | (24) difference(all_0_2_2, all_0_3_3) = all_13_0_9
% 2.76/1.37 | (25) difference(all_0_3_3, all_0_2_2) = all_13_1_10
% 2.76/1.37 | (26) union(all_13_1_10, all_13_0_9) = all_0_0_0
% 2.76/1.37 |
% 2.76/1.37 | Instantiating formula (17) with all_0_3_3, all_0_2_2, all_13_1_10, all_0_1_1 and discharging atoms difference(all_0_3_3, all_0_2_2) = all_13_1_10, difference(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 2.76/1.37 | (27) all_13_1_10 = all_0_1_1
% 2.76/1.37 |
% 2.76/1.37 | From (27) and (26) follows:
% 2.76/1.37 | (28) union(all_0_1_1, all_13_0_9) = all_0_0_0
% 2.76/1.37 |
% 2.76/1.37 | Instantiating formula (2) with all_0_0_0, all_13_0_9, all_0_1_1 and discharging atoms union(all_0_1_1, all_13_0_9) = all_0_0_0, ~ subset(all_0_1_1, all_0_0_0), yields:
% 2.76/1.38 | (29) $false
% 2.76/1.38 |
% 2.76/1.38 |-The branch is then unsatisfiable
% 2.76/1.38 % SZS output end Proof for theBenchmark
% 2.76/1.38
% 2.76/1.38 789ms
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